This invention relates generally to rotation sensors and particularly to fiber optic rotation sensors. Still more particularly, this invention relates to fiber optic rotation sensors having a high bias stability and repeatability.
A fiber optic ring interferometer typically comprises a loop of fiber optic material that guides counter-propagating light waves. After traversing the loop, the counter-propagating waves are combined so that they constructively or destructively interfere to form an optical output signal. The intensity of the optical output signal varies as a function of the interference, which is dependent upon the relative phase of the counterpropagating waves.
Fiber optic ring interferometers have proven to be particularly useful for rotation sensing. Rotation of the loop creates a relative phase difference between the counter-propagating waves in accordance with the well known Sagnac effect. The amount of phase difference is a function of the angular velocity of the loop. The optical output signal produced by the interference of the counter-propagating waves varies in intensity as a function of the rotation rate of the loop. Rotation sensing is accomplished by detecting the optical output signal and processing it to determine the rotation rate.
In order to be suitable for inertial navigation applications, a rotation sensor must have a very wide dynamic range. The rotation sensor must be capable of detecting rotation rates as low as 0.01 degrees per hour and as high as 1,000 degrees per second. The ratio of the upper and lower limits to be measured is approximately 10.sup.9.
It is well known that in many fiber optic systems it may be desirable to have light of a known polarization state at selected points. The output of some components is polarization dependent. Therefore, having a known polarization input to such components minimizes errors. The state of polarization is particularly important in a device such as an optical fiber rotation sensor. In a polarized optical fiber rotation sensing system, drift errors due to changes in polarization are determined by the quality of the polarizer.
Some familiarity with polarization of light and propagation of light within an optical fiber will facilitate an understanding of the present invention. Therefore, a brief description of the concepts used to describe the propagation and polarization of a light wave in a fiber will be presented.
An optical fiber comprises a central core and a surrounding cladding. The refractive index of the cladding is greater than that of the core. The core diameter is so small that light incident upon the core-cladding interface remains in the core by internal reflections.
It is well-known that a light wave may be represented by a time-varying electromagnetic field comprising orthogonal electric and magnetic field vectors having a frequency equal to the frequency of the light wave. An electromagnetic wave propagating through a guiding structure can be described by a set of normal modes. The normal modes are the permissible distributions of the electric and magnetic fields within the guiding structure, for example, a fiber optic waveguide. The field distributions are directly related to the distribution of energy within the structure. The normal modes are generally represented by mathematical functions that describe the field components in the wave in terms of the frequency and spatial distribution in the guiding structure. The specific functions that describe the normal modes of a waveguide depend upon the geometry of the waveguide. For optical fiber, where the guided wave is confined to a structure having a circular cross section of fixed dimensions, only fields having certain frequencies and spatial distributions will propagate without severe attenuation. The waves having field components that propagate unattenuated are called normal modes. A single mode fiber will propagate only one spatial distribution of energy, that is, one normal mode, for a signal of a given frequency.
In describing the normal modes, it is convenient to refer to the direction of the electric and magnetic fields relative to the direction of propagation of the wave. If only the electric field vector is perpendicular to the direction of propagation, which is usually called the optic axis, then the wave is a tranverse electric (TE) mode. If only the magnetic field vector is perpendicular to to the optic axis, the wave is a transverse magnetic (TM) mode. If both the electric and magnetic field vectors are perpendicular to the optic axis, then the wave is a transverse electromagnetic (TEM) mode.
None of the normal modes require a definite direction of the field components. In a TE mode, for example, the electric field may be in any direction that is perpendicular to the optic axis. The direction of the electric field vector in an electromagnetic wave is the polarization of the wave. In general, a wave will have random polarization in which there is a uniform distribution of electric field vectors pointing in all directions permissible for a given mode. If all the electric field vectors in a wave point in only a particular direction, the wave is linearly polarized. If the electric field consists of two orthogonal electric field components of equal magnitude phase shifted 90.degree. from each other, the electric field is circularly polarized, because the net electric field is a vector that rotates around the propagation direction at an angular velocity equal to the frequency of the wave. If the two linear polarizations are unequal or phased other than 90.degree. apart, the wave has elliptical polarization. In general, any arbitrary polarization can be represented by the sum of two orthogonal linear polarizations, two oppositely directed circular polarizations or two counter rotating elliptical polarizations that have orthogonal major axes.
The boundary between the core and cladding is a dielectric interface at which certain well-known boundary conditions on the field components must be satisfied. For example, the component of the electric field parallel to the interface must be continuous. A single mode optical fiber propagates electromagnetic energy having an electric field component perpendicular to the core-cladding interface. Since the fiber core has an refractive index greater than that of the cladding and light impinges upon the interface at angles greater than or equal to the critical angle, essentially all of the electric field remains in the core by internal reflection at the interface. To satisfy both the continuity and internal reflection requirements, the radial electric field component in the cladding must be a rapidly decaying exponential function. An exponentially decaying electric field is usually called the evanescent field.
The velocity of an optical signal depends upon the refractive index of the medium through which the light propagates. Certain materials have different refractive indices for different polarizations. A material that has two refractive indices is said to be birefringent. The polarization of the signal propagating along a single mode optical fiber is sometimes referred to as a mode. A standard single mode optical fiber may be regarded as a two mode fiber because it will propagate two waves of the same frequency and spatial distribution that have two different polarizations. Two different polarization components of the same normal mode can propagate through a birefringent material unchanged except for a velocity difference between the two polarizations.
Circular birefringence, linear birefringence, and elliptical birefringence are each described with reference to different polarization modes. If a material exhibits circular birefringence, the polarization of a light wave is expressed as a combination of two counter-rotating components. One of the circular polarizations is referred to as "right-hand circular" while the other is referred to as "left-hand circular". In a non-birefringent material both right hand and left hand circular polarizations travel at the same velocity. The counterrotating electric field vectors of the circular polarized components of the light represent the polarization modes for circular birefringence. If the light is linearly polarized, the circular polarization vectors are in phase with one another and are of equal amplitude. If the light is elliptically polarized, the circular polarization vectors are of unequal amplitudes or phase. In general, elliptically polarized light may have varying degrees of ellipticity; and the polarization may range from linearly polarized at one extreme to circularly polarized at the other extreme.
In a circularly birefringent material, the velocity of propagation of one circular polarization vector is greater than the velocity of propagation of the counterrotating polarization vector. Similarly, in a material that is linearly birefringent, the propagation velocity of the light in one of the linearly polarized modes is greater than the propagation velocity of the light in the other normal linearly polarized mode. Elliptical birefringence results when both linear birefringence and circular birefringence exist at a point in a material through which the light wave is propagating. The elliptical birefringence affects the polarization of light in a complex manner which depends, in part, upon the relative magnitudes of the linear birefringence and the circular birefringence.
In summary, any polarized light can be represented by two circularly polarized waves having proper phase and amplitude, two either elliptically rotating components or perpendicular linearly polarized electric field components.
Bias error is the primary source of error in using fiber optic Sagnac rings as rotation sensors. The bias of a rotation sensor is the signal output when there is no signal input. In the bias is constant, then it may be subtracted from the output signal when there is a signal input to determine the response of the rotation sensor to the input signal. However, the bias does not remain constant over time and temperature variations.
The principal source of bias error in fiber gyroscopes results from an imperfect polarizer and polarization cross coupling in the fiber. An ideal polarizer should have an infinite extinction ratio. The extinction ratio of a polarizer is the ratio of the intensity of the undesired polarization in the output signal to its intensity in the input signal. This error source was first identified by Kintner, Opt. Lett., Vol. 20, No. 6, p. 154(1981). Polarization instability manifests itself in optical interferometric systems in a manner analogous to signal fading in classical communications systems.
The maximum bias error may be expressed as EQU .phi..sub.e =2.epsilon..vertline.a.sub.B /a.sub.A .vertline..vertline..sup.t xy/t.sub.xx .vertline., (1)
where .phi..sub.e is the maximum phase bias error, .epsilon. is the polarizer field extinction ratio, a.sub.A and a.sub.B are the fields input to the polarizer from the source orthogonal and parallel to the polarizer transmission axis, t.sub.xy is the polarization cross coupling in the fiber loop, and t.sub.xx is the polarization retention for the fiber loop. Equation (1) is modified for fiber gyroscopes in which the input light is not completely polarized or if the input light is depolarized in the gyroscope. In such cases a.sub.B represents the electric field component input to the polarizer normal to the transmission axis and coherent with the electric field aligned with the transmission axis, and t.sub.xy represents the coherent polarization cross coupling in the fiber loop.
Fiber optic gyroscopes operating with polarized light require polarizers having extinction ratios in excess of 100 dB to keep bias errors below 0.01 deg/hr. Fiber optic gyroscopes using unpolarized light require extinction ratios in the 60-100 dB range and require the use of high quality polarization maintaining (PM) fiber throughout the gyroscope.
A linear polarization state in a fiber optic rotation sensor is typically achieved with some type of linear polarizer such as the fiber optic polarizer described in U.S. Pat. No. 4,386,822 to Bergh. The polarization state input to the polarizer is arbitrary in general. The polarizer couples light of undesired polarizations out of the fiber and permits light having only a selected desired polarization to propagate through the fiber. Bergh discloses a fiber optic polarizer including a length of optical fiber mounted in a curved groove in a quartz substrate. The substrate and a portion of the optical fiber are ground and polished to remove a portion of the cladding from the fiber to form an interaction region. The portion of the fiber in the groove is convexly curved as viewed looking toward the polished surface. The birefringent crystal is mounted on the substrate over the interaction region in close proximity to the core of the fiber optic material. The crystal is positioned to partially intersect the path of light propagating in the optical fiber so that evanescent field coupling couples light of undesired polarizations from the optical fiber into the crystal.
The birefringent crystal has different wave velocities for waves of different polarizations. With polarizations for which the wave velocity in the crystal is less than the wave velocity in the optical fiber, the light carried by the optical fiber excites a bulk wave in the crystal, which causes light to escape from the optical fiber into the crystal. No bulk wave is excited in the crystal for polarizations having wave velocities in the crystal greater than in the fiber so that light having such polarizations remains guided within the optical fiber. The refractive indices of the crystal are such that a wave having a polarization along one of the principal axes of the crystal will propagate more slowly in the crystal than the optical fiber; and a wave having a polarization along a second principal axis will propagate at a greater speed in the crystal than in the optical fiber.
An improved apparatus for producing light of a known polarization includes a polarization controller placed in the fiber between the light source and the polarizer with the polarization controller being adjusted to provide light of a desired polarization for input into the polarizer. However, in a typical system the polarization state input to the polarization controller varies due to the environmental sensitivities of the optical fiber. Variations in temperature and pressure, vibrations, and aging of the materials may cause significant changes in the polarization output from the polarization controller to the polarizer. Therefore, in a system which includes a polarization controller fixed to vary the polarization of light input by a predetermined amount, the time varying polarization of the light input to the polarization controller causes signal fading.
Other problems associated with prior polarizers are the result of using naturally occurring crystals. Each naturally occurring crystal has only certain refractive indices determined by the crystalline structure, therefore naturally occurring crystals may not have the desired refractive indices. Another difficulty with naturally occurring crystals involves adequately bonding them to the substrate. The crystals are not environmentally stable, which is still another source of error.
A second improved polarizer includes a feedback system for detecting the light coupled out of the fiber, which represents an error signal. The error signal is used to adjust the polarization of the light input to the polarizer to minimize the amount of light coupled out of the system.
The effectiveness of such polarizers is highly dependent upon the refractive index of the crystal. Unfortunately, the refractive indices of birefringent crystals are highly temperature-sensitive. In order to be suitable for inertial guidance applications, a rotation sensor must have a high degree of temperature stability because such rotation sensors must be operable over a range of temperature from -55 degrees Celsius to +125 degrees Celsius, according to standard specifications.
Making stable polarizers with 100+ dB extinction ratios is difficult and using high quality polarization maintaining fiber throughout the gyroscope is expensive due to the high cost of the fiber. However, significant reductions in polarizer extinction ratio requirements are possible if the light incident on the polarizer normal to the transmission axis has a low degree of coherence with the light parallel to the transmission axis and if the fiber loop has small coherent cross coupling.
The coherence between the input components of the electric field referenced to the polarizer axis and coherent cross coupling in the loop can be reduced by using a polarization maintaining fiber and a broadband source. Coherence still results if the principal axes of the fibers are not aligned precisely with the polarizer axis. Aligning the fiber axes with the polarizer axis is difficult with fiber because of the difficulty in locating the principal axis and in maintaining the principal axis in a known orientation during fabrication of the gyroscope.
Light launched coherently into both axes of a polarization maintaining fiber will have its coherence reduced to 1% in a distance of 0.3 to 1.0 meter. Longer lengths of fiber will not reduce the coherence below 1% because of competing processes which restore the coherence due to waveguide imperfections and differential loss between the two polarizations. These sources are essentially beyond the control of the manufacturer. The only way to reduce the coherence between the two polarizations is to increase the birefringence of the polarization maintaining fiber. This increased birefringence causes the polarizations to lose coherence in a shorter distance and prevents the competing processes from building up to a high level. This results in a smaller degree of coherence between the polarizations.
Significantly increasing the birefringence of the polarization maintaining fiber is not practical at the present time. Such fibers usually have a stress-induced birefringence or have an elliptical core, which provides birefringence. Additional stress induced birefringence would shatter the fiber, and highly ellipsoidal cores would cause unacceptably high loss.
Precise alignment of the polarizer axes with the waveguide principal axes and increased birefringence resulting in a lower degree of coherence between the polarizations can be realized by fabricating the loop coupler and polarizer on an LiNbO.sub.3 substrate using integrated optical techniques. The polarization uses high quality (i.e., high extinction ratio) polarization maintaining fiber in the fiber loop and between an SLD/photodetector and the LiNbO.sub.3 chip. Optical damage is still a problem in LiNbO.sub.3. The long term stability of integrated optics circuits in LiNbO.sub.3 is still in serious question. In addition, the high scattering loss (0.1-0.5 dB/cm) in integrated optics circuits in LiNbO.sub.3 limits the performance of such fiber optic gyroscopes in terms of noise, bias error, and scale factor error.